I have the following observation about solid wood warping when exposed to humidity/heat...
Years ago my kids' school replaced their chalkboards with whiteboards and the chalk rails that ran along the bottom of the chalkboards were removed and discarded. They were essentially 2x6x10-foot long straight grain mahogany. After determining no one wanted them as they sat in the rain, I took all of them, but not having an immediate project I stashed them outside my garage, in the rain and weather, for about ten years.
My wife and I were looking to change our kitchen table. Reclaimed wood tables were running in the multi-$thousands from Pier 1 and the usual suppliers. I put one of the chalk rails on the sawhorses and ran the belt sander over it. The coarse belt took off a few 32nds of gray surface wood and underneath it was pristine. I cut six boards to about 7 feet, cleaned them up, rabetted joints and epoxied six of them together, secured (pair by pair) with pipe clamps. Finished with a fill coat of epoxy and a couple coats of poly. I wasn't careful to align the grain on each of the six boards, so flattening was a bit of a pain, but the finished boards are about 1.25" thick.
Over 15 years we've had the table in our kitchen in front of the big window with a great view of Diamond Head. The table receives daily exposure to sun and heat - in Hawaii the typical temps range run from mid-60s to low 90s, with humidity to match. NEVER ONCE have I seen any evidence of warping or distortion.
The moral of the story seems to be (in my experience) that well-acclimated solid wood, sealed against humidity changes, does not warp. I'll expect, though, that thin strips of wood, unsupported by a stiff base, could well distort. Sadly I have some 1/4" thick koa paneling that has done so and I'm not sure what I'll do with that, but I hoard koa, so I'll probably die in possession and my kids will throw it in the trash.